Open problems solved
10
Fields of mathematics covered
8
Compute cost to solve all ten
approx. 2,000 USD
Longest time any problem had been open
over 25 years
Length of accompanying manuscript
249 pages
Lean 4 machine-checkable proofs published
10 of 10
What Is Astra
OpenAI's next major model family has a name: Astra. But it did not arrive with a press conference or a benchmark leaderboard. On 1 August 2026, researcher Noam Brown pushed ten machine-checkable mathematical proofs to GitHub and wrote a brief post calling Astra "our next major model." The problems it had solved had seen no meaningful progress for at least a decade. Most had been open for much longer. Astra is described as a "long-horizon" system, designed to work on extended tasks autonomously rather than answer questions in a single exchange. The public release date, model size, context window, and API price are all unknown. What is known is that an internal version of Astra, still unreleased, cracked ten problems across eight distinct fields of mathematics and theoretical computer science.
How Astra Proved Ten Unsolved Problems
Field
/
Step
The non-sofic groups result (Gromov, 1999) is considered the single most significant of the ten. Non-sofic groups are mathematical objects that cannot be approximated by finite permutation groups. Their existence had been conjectured but never proven. Astra produced a constructive proof.
The total compute cost for all ten results was approximately 2,000 USD at Sol API rates, the same model family used in OpenAI's consumer products. Elon Musk responded to the announcement on X with the words: "Welcome to the Singularity."
What This Changes
The significance is not just the results themselves. Every prior AI maths milestone (AlphaProof, GPT-5 solving competition problems) involved closed-form answers to well-defined problems. Astra's ten results are open-ended contributions: new constructions, new bounds, and new disproofs that professional mathematicians had not produced. The Lean 4 certificates change the epistemology of mathematical discovery. Instead of waiting months for peer review, anyone can run the certificate and confirm the proof is valid in minutes. If this scales, the pace of mathematical progress could accelerate in ways that are difficult to project. The cost of a decade of unsolved problems just dropped to roughly two thousand dollars.
"These are big news. More significant than the unit distance counterexample announced in May.
"Thomas Bloom
Astra has not launched publicly. OpenAI has not confirmed a release date, model size, context window, or price. The internal version that produced these results may differ substantially from the product that eventually ships. Polymarket puts an August 31 public release at approximately 24 percent probability.
